3211. The Sum of an Infinite Series Deduced from a Numerical Differentiation Formula

1969 ◽  
Vol 53 (383) ◽  
pp. 61
Author(s):  
M. P. Hyde
Keyword(s):  
Infinite Series ◽  
Numerical Differentiation ◽  
Differentiation Formula ◽  
Numerical Differentiation Formula

scholarly journals Numerical differentiation on scattered data through multivariate polynomial interpolation

2021 ◽  
Author(s):  
Francesco Dell’Accio ◽  
Filomena Di Tommaso ◽  
Najoua Siar ◽  
Marco Vianello
Keyword(s):  
Polynomial Interpolation ◽  
Numerical Differentiation ◽  
Scattered Data ◽  
Monomial Basis ◽  
Multivariate Polynomial Interpolation ◽  
Differentiation Formula ◽  
Local Polynomial ◽  
Leja Points ◽  
Derivatives Of ◽  
Numerical Differentiation Formula

AbstractWe discuss a pointwise numerical differentiation formula on multivariate scattered data, based on the coefficients of local polynomial interpolation at Discrete Leja Points, written in Taylor’s formula monomial basis. Error bounds for the approximation of partial derivatives of any order compatible with the function regularity are provided, as well as sensitivity estimates to functional perturbations, in terms of the inverse Vandermonde coefficients that are active in the differentiation process. Several numerical tests are presented showing the accuracy of the approximation.

scholarly journals Added Masses and Forces on Two Bodies Approaching Central Impact in an Inviscid Fluid

1992 ◽  
Vol 36 (02) ◽  
pp. 99-122
Author(s):  
L. Landweber ◽  
A. Shahshahan
Keyword(s):  
Integral Equation ◽  
Exact Solution ◽  
Infinite Series ◽  
Numerical Differentiation ◽  
The Other ◽  
Asymptotic Formulas ◽  
Inviscid Fluid ◽  
Interaction Forces ◽  
Added Masses ◽  
Two Bodies

An integral-equation procedure has been developed to determine interaction forces on two bodies approaching central impact in an inviscid fluid. The accuracy of the results from that procedure is evaluated by applying it to a pair of circles and a pair of spheres for which exact solutions are available. A second purpose was to refine the procedure so that accurate solutions could be obtained at closer distances between the bodies. In the first part of this work, the classical theory is extended by deriving truncation corrections for the infinite series representing the exact solution and asymptotic formulas for computing interaction forces at small gaps. In the second part, two problems were resolved: one on the treatment of the sharp peaks of the integrands when the gap between the bodies was small, the other on reducing the errors in the numerical differentiation required to evaluate the forces. Results for various combinations of circle pairs, for equal spheres, and for an elliptical cylinder approaching a circular one are presented. A new relation between the interaction forces on a wall and on a body moving normal to it is presented. Addendum published in 1994 Volume 38, Issue 2 (June), pages 172–173, is included.

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